Great Fun Trilegiant Corporation Invitation to apply for cash rebate Stamford, Connecticut

Received a letter from Great Fun inviting me to claim $20 cash back on my recent purchase. I couldn't  think of what I had recently purchased, & had no idea who they are. The address on the letter is PO Box 41246, Nashville, TN 37204.The back of the letter has a form to fill out asking for Today's Date, First Name, Last Name, Address, Apt.#,/Building #, City, State, zip. Terms
& Conditions. I'm supposed to fill out the form & send to Rebate Department, PO Box 6170, Westerville, OH 43086-6170 - a different address from the letterhead. The fine print in the body of the letter says Great Fun is a service provided by Trilegiant Corp, registered mark of Affinion Publishing, LLC.  I Googled them, got their company information & phone number.
http://investing.businessweek.com/research/stocks/private/snapshot.asp?privcapId=1528213 (link to Bloomberg News article. This link also mentions they're being sued). I called Trilegiant & asked where/how they got my information and what is the rebate about. Carmen in customer relations told me it was from my recent internet purchase of tickets on Allegiant Airlines (their travel service is offered when booking -  I declined). I certainly do not intend to give them any further information. I don't trust them. They may start  charging my credit card for some service I don't want. I hope that calling their corporate office doesn't result in being inadvertently enrolled in any of their programs, even though I declined when booking my flight. I'll be watching my credit card closely.  Buyers must beware & be aware. When you get anything by mail, phone or internet that sounds too good, do a Google search. You can find almost anything on Google.